The ordinal and binary models considered in this chapter, whether estimated
using the Classical or the Bayesian techniques, provide information on the average
probability of outcomes conditional on the covariates. However, interests in
the quantiles of the response variable as a robust alternative to mean
regression have grown enormously since the introduction of quantile
regression in [1]}. Quantile modeling gained further
momentum with the development of Bayesian quantile regression by
[2]}, where the authors create a working likelihood by
assuming that the errors follow an asymmetric Laplace (AL) distribution
[3]}. Binary quantile regression was proposed by
[4]} and its Bayesian formulation was presented by
[5]}. [6]} introduced Bayesian quantile
regression with ordinal responses and estimated the model using MCMC
techniques. A flexible form of Bayesian ordinal quantile regression was
proposed in [7]}. Some recent research on ordinal and
binary quantile regression in the panel/longitudinal set up include
[8]}, [9]}, and
[10]}. Two applied studies employing ordinal and binary
quantile framework are [11]} and [12]},
respectively. Interested readers may explore the above mentioned papers and
references therein to develop a thorough understanding on ordinal and binary
quantile modeling and their applications.
